= Antiunitary operator
{title2=$\langle Au,Av\rangle=\overline{\langle u,v\rangle}$}
{wiki}
= Antiunitarity
{synonym}
An antiunitary operator between complex <Hilbert spaces> is a surjective <antilinear map> satisfying the displayed <inner product> identity. It preserves <norms> but conjugates scalars. In a chosen <orthonormal basis> it is $UK$, with $U$ a <unitary operator> and $K$ coefficientwise <complex conjugation>. Conversely any such $UK$ is antiunitary. Antilinearity by itself does not preserve norms.
Back to article page
